diff --git a/protocol/protocol.tex b/protocol/protocol.tex index 62496dd8..4c98da22 100644 --- a/protocol/protocol.tex +++ b/protocol/protocol.tex @@ -6220,8 +6220,8 @@ Let $\ParamG{b} := 3$. (\hairspace $\ParamG{q}$ and $\ParamG{r}$ are prime.) -Let $\GroupG{1}$ be the group of points on a Barreto--Naehrig curve $\CurveG{1}$ over -$\GF{\ParamG{q}}$ with equation $y^2 = x^3 + \ParamG{b}$. +Let $\GroupG{1}$ be the group of points on a Barreto--Naehrig (\cite{BN2005}) +curve $\CurveG{1}$ over $\GF{\ParamG{q}}$ with equation $y^2 = x^3 + \ParamG{b}$. This curve has embedding degree 12 with respect to $\ParamG{r}$. Let $\GroupG{2}$ be the subgroup of order $r$ in the sextic twist $\CurveG{2}$ of @@ -6386,8 +6386,8 @@ Let $\ParamS{b} := 4$. (\hairspace $\ParamS{q}$ and $\ParamS{r}$ are prime.) -Let $\GroupS{1}$ be the group of points on a Barreto--Lynn--Scott curve $\CurveS{1}$ over -$\GF{\ParamS{q}}$ with equation $y^2 = x^3 + \ParamS{b}$. +Let $\GroupS{1}$ be the group of points on a Barreto--Lynn--Scott (\cite{BLS2002}) +curve $\CurveS{1}$ over $\GF{\ParamS{q}}$ with equation $y^2 = x^3 + \ParamS{b}$. This curve has embedding degree 12 with respect to $\ParamS{r}$. Let $\GroupS{2}$ be the subgroup of order $\ParamS{r}$ in the sextic twist $\CurveS{2}$ of @@ -8855,6 +8855,7 @@ found by Brian Warner. \item Specify support for \cite{BIP-111} (the \texttt{NODE\_BLOOM} service bit) in network protocol version $170004$. \item Give references \cite{Vercauter2009} and \cite{AKLGL2010} for the optimal ate pairing. + \item Give references for BLS \cite{BLS2002} and BN \cite{BN2005} curves. \item Define $\KASproutDerivePublic$ for $\KASproutCurve$. \item Caveat the claim about \noteTraceabilitySet in \crossref{overview} and link to \cite{Peterson2017} and \cite{Quesnelle2017}. diff --git a/protocol/zcash.bib b/protocol/zcash.bib index dd99a3b2..218b7ae7 100644 --- a/protocol/zcash.bib +++ b/protocol/zcash.bib @@ -75,6 +75,26 @@ Lecture Notes in Computer Science; Springer, 2013.}, Last revised September~12, 2011.} } +@misc{BLS2002, + presort={BLS2002}, + author={Paulo Barreto and Ben Lynn and Michael Scott}, + title={Constructing {E}lliptic {C}urves with {P}rescribed {E}mbedding {D}egrees}, + url={https://eprint.iacr.org/2002/088}, + urldate={2018-04-20}, + howpublished={Cryptology ePrint Archive: Report 2002/088. +Last revised February~22, 2005.} +} + +@misc{BN2005, + presort={BN2005}, + author={Paulo Barreto and Michael Naehrig}, + title={Pairing-{F}riendly {E}lliptic {C}urves of {P}rime {O}rder}, + url={https://eprint.iacr.org/2005/133}, + urldate={2018-04-20}, + howpublished={Cryptology ePrint Archive: Report 2005/133. +Last revised February~28, 2006.} +} + @misc{Vercauter2009, presort={Vercauter2009}, author={Frederik Vercauteren},